The Feng-Rao bound gives good estimates of the minimum distance of a large class of codes. In this work we are concerned with the problem of how to extend the Feng-Rao bound so that it deals with all the generalized Hamming weights. The problem was solved by Heijnen and Pellikaan in [7] for a large family of codes that includes the duals of one-point geometric Goppa codes and the q-ary Reed-Muller codes, but not the Feng-Rao improved such ones. We show that Heijnen and Pellikaan's results holds for the more general class of codes for which the traditional Feng-Rao bound can be applied. We also establish the connection to the Shibuya-Sakaniwa bound for generalized Hamming weights ([15], [16], [17], [18], [19] and [20]). More precisely we show that the Shibuya-Sakaniwa bound is a consequence of the extended Feng-Rao bound. In particular the extended Feng-Rao bound gives always at least as good estimates as does the Shibuya-Sakaniwa bound. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Geil, O., & Thommesen, C. (2006). On the feng-rao bound for generalized hamming weights. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3857 LNCS, pp. 295–306). https://doi.org/10.1007/11617983_29
Mendeley helps you to discover research relevant for your work.